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How many of the first 500 positive integers are multiples of integers 3, 4 or 5?

 May 24, 2024
 #1
avatar+591 
0

We can find the count of multiples of 3, 4 and 5 upto 500 using the following logic. We iterate through all numbers from 1 to 500 and check if the number is divisible by 3, 4 or 5. If the number is divisible by any of these numbers, we increment the count.

 

Here's the code for this logic:

 

Python

 

# Count multiples of 3, 4, and 5 up to 500 count = 0 # Iterate through the first 500 positive integers for num in range(1, 501): # Check if the number is a multiple of 3, 4, or 5 if num % 3 == 0 or num % 4 == 0 or num % 5 == 0: count += 1 print(count)

 

 

This code outputs the following:

320

 

There are total 320 multiples of 3, 4 or 5 up to 500.

 May 24, 2024
 #3
avatar+820 
+2

I think there was a slight error in your code for python. 

 

I followed your logic and iteration, and the answer turned out to be 300. 

 

I don't know if I made an error, but it does match with the answer I got using plain logic. 

Here's my explenation for the problem. 

 

First, let's find how many of each number there are. 

 

500/3 = 166.66, so there are 166 integers. 

 

500/4 = 125, so there are 125 integers.

 

500/5 = 100, so there are 100 integers. 

 

Next, we must find the duplicates of numbers. 

 

3*4 = 12 

3*5 = 15

4*5 = 20

 

500/12 = 41.67, so there are 41 integers

500/15 = 33.33, so there are 33 itnegers. 

500/20 = 25, so there are 25 integers. 

LCM = 3*4*5 = 60. 

 

500/60 = 8.33, so there are 8 integers. 

 

166+125+100-41-33-25+8 = 300. 

 

Let me summarize. 

First, we find how many numbers are divisble by 3,4,5. However, there are duplicates, so we subtract those, before adding the LCM!

 

Thanks! :)

NotThatSmart  May 24, 2024
 #2
avatar+820 
+2

First, let's find how many of each number there are. 

 

500/3 = 166.66, so there are 166 integers. 

 

500/4 = 125, so there are 125 integers.

 

500/5 = 100, so there are 100 integers. 

 

Next, we must find the duplicates of numbers. 

 

3*4 = 12 

3*5 = 15

4*5 = 20

 

500/12 = 41.67, so there are 41 integers

500/15 = 33.33, so there are 33 itnegers. 

500/20 = 25, so there are 25 integers. 

LCM = 3*4*5 = 60. 

 

500/60 = 8.33, so there are 8 integers. 

 

166+125+100-41-33-25+8 = 300. 

 

Let me summarize. 

First, we find how many numbers are divisble by 3,4,5. However, there are duplicates, so we subtract those, before adding the LCM!

 

Thanks! :)

 May 24, 2024

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